1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sladkaya [172]
2 years ago
12

The hypotenuse of a right triangle is 13 ft long. The longer leg is 7 ft longer than the shorter leg. Find the side lengths of t

he triangle.
Mathematics
1 answer:
Scrat [10]2 years ago
8 0

Answer:

The shorter leg is five feet, the longer leg is 12 feet, and the hypotenuse is 13 feet.

Step-by-step explanation:

Let the shorter leg be <em>x</em>.

Since the longer leg is seven feet longer than the shorter leg, the length of the longer leg can be modeled by (<em>x</em> + 7).

Since the triangle is a right triangle, we can use the Pythagorean Theorem, given by:

a^2+b^2=c^2

Where <em>a</em> and <em>b</em> are the side lengths and <em>c</em> is the hypotenuse.

The hypotenuse is 13 and the legs are <em>x</em> and (<em>x</em> + 7). Substitute:

(x)^2+(x+7)^2=(13)^2

Square:

x^2+x^2+14x+49=169

Simplify:

2x^2+14x-120=0

We can divide both sides by two:

x^2+7x-60=0

Factor:

(x-5)(x+12)=0

Zero Product Property:

x-5=0\text{ or }x+12=0

Solve for each case:

x=5\text{ or } x=-12

Since lengths cannot be negative, we can ignore the negative answer. So, our only solution is:

x=5

The shorter leg is five feet, the longer leg will be (5 + 7) or 12 feet. And the hypotenuse is 13 feet as given.

You might be interested in
The pair of triangles that are congruent by the ASA criterion is . The pair of triangles that are congruent by the SAS criterion
anzhelika [568]

Answer:

The pair of triangles that are congruent by the ASA criterion isΔ ABC and Δ XYZ.

The pair of triangles that are congruent by the SAS criterion is Δ BAC and ΔRQP.


Step-by-step explanation:

Two triangles are congruent by ASA property if any two angles and their included side are equal in both triangles .In triangles Δ ABC and Δ XYZ the equal side 5 is between the two equal angles. So these triangles are congruent by ASA criterion.

Two triangles are congruent by SAS if  two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle .In triangles  Δ BAC and ΔRQP. the included angles A and Q are equal and hence the triangles are congruent by SAS criterion.

5 0
3 years ago
Read 2 more answers
If y/z=4/7, then z/y=
topjm [15]

Answer:

z/y = 7/4

Step-by-step explanation:

In y/z = 4/7, the numerator and denominator correspond with each other

So, y =4 and z = 7

5 0
2 years ago
7(2 + 6 – 4d) = pl help me I don’t get it
Svetach [21]

Answer:

Step-by-step explanation:

1. 1 Simplify  2+6-4d to  -4d+8.

7 ( -4d + 8)

therefor, the answer is, 7( -4d + 8)

7 0
3 years ago
Read 2 more answers
Please help first person to answer correctly gets 50 and marked as brainly
jeka94

Answer:

b

HOPE THIS HELPS!!

6 0
2 years ago
The minute hand on a watch is 2.00 cm in length. what is the displacement vector of the tip of the minute hand
olchik [2.2K]
The displacement vector is a vector which gives the point's current position with reference to other points apart from points from the origin. The given length here of the minute hand is the radius and the distance can be written as,
                                       r∠θ
which means that the position can be described by the θ.
3 0
3 years ago
Other questions:
  • Julio has $127 in his bank account. He gets $30 for his birthday. He also has a part-time job that pays $9 per hour. How many ho
    5·2 answers
  • You are mowing a lawn. After 12 minutes, 52% of the lawn still needs mowed. How long does it take to mow the entire lawn? Write
    11·1 answer
  • Write various of the equation of a line that passes through (-6, 3) and has a slope of - 1/3
    5·1 answer
  • Lucille has a collection of more than 500 songs on her phone that have a mean duration of 215 seconds
    15·1 answer
  • Plzzzzzzz helpppp right answer gets brainly
    8·2 answers
  • A bag of marbles has 5 blue marbles, 3 red marbles, and 6 yellow marbles. A marble is drawn from the bag at
    8·2 answers
  • The two parallelograms in the graph below are similar. Which sequence of transformations proves that the parallelograms are simi
    14·1 answer
  • Please help me, choose the right one
    5·2 answers
  • Triangle ABC is dilated to create triangle DEF on a coordinate grid. You are given that angle A is congruent to angle D. What ot
    8·1 answer
  • Question is in the picture
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!